A103437 Sum_{i>=1} (i^n*Lucas(i)/2^i).

4, 22, 210, 2974, 56130, 1324222, 37489410, 1238235454, 46740118530, 1984855550782, 93653819396610, 4860878501987134, 275227990564092930, 16882335978752910142, 1115211301788480951810, 78930528072274523870014

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..356

Formula

From Robert Israel, Jan 24 2017: (Start)

a(n) = polylog(-n, (sqrt(5)+1)/4) + polylog(-n, (-sqrt(5)+1)/4).

E.g.f.: 2*exp(x)*(exp(x)+1)/(4-2*exp(x)-exp(2*x)). (End)

a(n) ~ n! / (log(sqrt(5)-1))^(n+1). - Vaclav Kotesovec, Jan 24 2017

Maple

V:=2*exp(x)*(exp(x)+1)/(4-2*exp(x)-exp(2*x)):
S:= series(V, x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Jan 24 2017

Crossrefs

Cf. A000032.

Sequence in context: A183274 A303330 A280828 * A215201 A063380 A113385

Adjacent sequences: A103434 A103435 A103436 * A103438 A103439 A103440

Keyword

nonn

Author

Ralf Stephan, Feb 08 2005

Status

approved